Question

after your encounter with the siren, you visit a nearby ice cream truck and treat yourself to one of those spongebob bars with gumballs for eyes (because, apparently, you are 10 years old in this problem). you then begin riding your bike away from the stationary ice cream truck as it begins playing music. you hear a frequency of 325 hz and your friend, who is riding his bike at 8 m/s (away from the truck), hears a frequency of 320 hz. how fast are you traveling (in m/s)?

Answer 1

To calculate your speed, we can use the formula for the Doppler effect. Therefore, the speed is 4.85 m/s.

To calculate the speed at which you are traveling, we can use the formula for the Doppler effect. The formula is:

f' = f(v + vr) / (v - vs)

Where:

f' is the observed frequency

f is the actual frequency

v is the speed of sound

vr is the velocity of the receiver (you)

vs is the velocity of the source (ice cream truck)

Given that you hear a frequency of 325 Hz and your friend hears a frequency of 320 Hz, we can plug in these values into the formula. Let's assume the speed of sound is 335 m/s:

325 = f(335 + vr) / (335 - vs)

320 = f(335 + 8) / (335 - vs)

Simplifying these equations, we get:

vr = (5/335)f

vs = (5/335)f - 8

We can solve for f by substituting the known values from the problem into the equations:

vr = (5/335)(325) = 4.85 m/s

vs = (5/335)(325) - 8 = -3.15 m/s

Therefore, your velocity (vr) is 4.85 m/s.

Answer 2

To calculate your speed, we can use the formula for the Doppler effect. By substituting the given values into the equation, you can determine that your speed is 343 m/s.

Step-by-step explanation:

To determine your speed, we can use the formula for the Doppler effect:

Observed Frequency = Actual Frequency * (Speed of Sound + Speed of Observer) / (Speed of Sound + Speed of Source)

In this case, you are the observer and the ice cream truck is the source. Let's plug in the given values: Observed Frequency = 320 Hz, Actual Frequency = 325 Hz, Speed of Observer (your friend) = 8 m/s, and Speed of Sound = 335 m/s.

Solving for your speed:

Speed of Sound + Speed of Observer = (Observed Frequency * Speed of Source) / Actual Frequency - Speed of Sound

Substituting the given values:

Speed of Sound + 8 m/s = (320 Hz * 0 m/s) / 325 Hz - 335 m/s

Simplifying the equation:

Speed of Sound + 8 m/s = 0 m/s - 335 m/s

Speed of Sound + 8 m/s = -335 m/s

Speed of Sound = -343 m/s

Therefore, your speed is 343 m/s.